# How many of different connected graphs with n vertices? Excluding of isomorphic graphs.

Given $$n$$ vertices, the question is to answer how many different connected graphs exist?

For example, $$f(1)=1,f(2)=1,f(3)=2,f(4)=6 \cdots$$.

Here I exclude the isomorphic graphs.

I know there is a sequence http://oeis.org/A001349

But can anyone try to explain how to calculate the sequence?

• Are you looking for a closed formula? – TheHolyJoker Jan 17 '20 at 19:51
• The link to the oeis entry contains several references that should answer your question. – Morgan Rodgers Jan 17 '20 at 19:58
• @TheHolyJoker Yes, is there a closed formula? – Kimmi Jan 17 '20 at 20:17
• The OEIS sequence A000088 "Number of onnected graphs with n nodes" has formulas and computer code. The sequences A000088 and A001349 are connected by the Euler transform. – Somos Jan 17 '20 at 20:47
• This MSE link may prove useful. – Marko Riedel Jan 18 '20 at 19:01